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3 years ago

6

Mathematics

1 answer:

soldi70 [24.7K]3 years ago

3 0

Answer:

9

Step-by-step explanation:

f(x) = 4x- 11

f(5) = 4(5) - 11

f(5) = 20- 11

f(5) = 9

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Find the weight of the cast iron shape shown below at 0.26 pounds per cubic inch. (round to the nearest pound). The height of th

weqwewe [10]

Answer:

640 pounds

Step-by-step explanation:

The rest of the question is the attached figure

So, the total volume = V(cylinder ) + V(cone)

The volume of cylinder = π r² h

The volume of cone = π r² h/3

Both of the cylinder and the cone have the same diameter = 14 inches

So, the radius = 14/2 = 7 inches

The height of the cylinder is 13 inches and the height of the cone is 9 inches.

So, The volume of cylinder = π r² h = π * 7² * 13 = 2,001.2 in³

And The volume of cone = π r² h/3 = π * 7² * 9/3 = 461.8 in³

So, the total volume = 2,001.2 + 461.8 = 2,463 in³

So, the total weight = 0.26 pounds per cubic inch times the total volume

= 0.26 * 2463 = 640.38 pounds

= 640 pounds (to the nearest pound)

6 0

3 years ago

The smallest exterior angle of a polygon is 40degrees the largest exterior angle is 80 degrees a) what is the smallest possible

love history [14]

Answer:

a) The smallest possible number of sides of the polygon is a regular polygon with 5 sides

b) The largest possible number of sides of the polygon is a regular polygon with 9 sides

Step-by-step explanation:

a) The smallest exterior angle of the polygon = 40°

The largest exterior angle of the polygon = 80°

Therefore, we have the interior angles are;

The smallest interior angle of the polygon = 180° - 40° = 140°

The largest interior angle of the polygon = 180° - 80° = 100°

Therefore, we have

The interior angles of a regular polygon are given by the following formula;

$Interior \ angle =\dfrac{(n-2) \times 180 ^{\circ}}{n}$

For an interior angle of 100°, we have;

$100^{\circ} =\dfrac{(n-2) \times 180 ^{\circ}}{n}$

100/180 × n = n - 2

2 = n - 100/180 × n = 4/9·n

2 = 4/9·n

n = 18/4 = 4.5

Therefore, given that a square has an interior angle of 90° we have the smallest possible number of sides polygon = 5 sides

b) For 140°, we have;

$140^{\circ} =\dfrac{(n-2) \times 180 ^{\circ}}{n}$

140/180 × n = n - 2

2 = n - 140/180 × n = 2/9·n

2 = 2/9·n

n = 18/2 = 9

n = 9 sides

Therefore, the largest possible number of sides = 9 Sides.

4 0

3 years ago

jackie and her friend were having a garage sale. during the first two hours of the garage sale 32 bookks were sold. the number o

kirill [66]

How many friends are there

7 0

3 years ago

7/18 ratio in simplest form

mel-nik [20]

It can go to 3.5/9 but thats as low as it can go

4 0

3 years ago

Find AA and BB that make the equation true. Verify your results.

CaHeK987 [17]

Answer:

a. A = -1 and B = 1

b. A = 7 and B = -5

Step-by-step explanation:

$\frac{A}{x+1} +\frac{B}{x-1} = \frac{2}{x^2-1}$

$\frac{A*(x-1)+B*(x+1)}{(x+1)*(x-1)} = \frac{2}{x^2-1}$

$\frac{Ax - A + Bx + B}{x^2 -1} = \frac{2}{x^2-1}$

To the equation be true, the "x-parts" and "nonx-parts" mist be the same, so:

Ax + Bx = 0

(A + B)x = 0

A + B = 0

A = -B

B - A = 2

B - (-B) = 2

2B = 2

B = 1 and A = -1

$\frac{A}{x+3} + \frac{B}{x +2} = \frac{2x -1}{x^2+5x+6}$

$\frac{A*(x+2) + B*(x+3)}{(x+3)*(x+2)} = \frac{2x-1}{x^2+5x+6}$

$\frac{Ax + 2A + Bx + 3B}{x^2 + 5x + 6} = \frac{2x-1}{x^2+5x+6}$

To the equation be true, the "x-parts" and "nonx-parts" mist be the same, so:

Ax + Bx = 2x

(A + B)x = 2x

A + B = 2

A = 2 - B

2A + 3B = -1

2*(2-B) + 3B = -1

4 - 2B + 3B = -1

B = -5 and A = 2 - (-5) = 7

5 0

3 years ago